7,128,000 and 11,880,000: All the common factors (divisors) and prime factors of the integer numbers

The common factors of numbers 7,128,000 and 11,880,000

The common factors (divisors) of numbers 7,128,000 and 11,880,000 are all the factors (divisors) of their 'greatest (highest) common factor (divisor)'.

Note

Factor of a number A: a number B that when multiplied with another C produces the given number A. Both B and C are factors of A.



Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd. Follow the two steps below.

Integer numbers prime factorization:

Prime Factorization of a number: finding the prime numbers that multiply together to make that number.


7,128,000 = 26 × 34 × 53 × 11;
7,128,000 is not a prime, is a composite number;


11,880,000 = 26 × 33 × 54 × 11;
11,880,000 is not a prime, is a composite number;


* Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself.
* A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.




Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd

Multiply all the common prime factors, by the lowest exponents (if any).


Greatest (highest) common factor (divisor):


gcf, hcf, gcd (7,128,000; 11,880,000) = 26 × 33 × 53 × 11 = 2,376,000;




Find all the factors (divisors) of the GCF (HCF, GCD)

2,376,000 = 26 × 33 × 53 × 11


Get all the combinations (multiplications) of the prime factors of GFC (HCF, GCD) that give different results.


When combining the prime factors also consider their exponents.


Also add 1 to the list of factors (divisors). Any number is divisible by 1.


All the factors (divisors) are listed below, in ascending order.



Factors (divisors) list:

neither a prime nor a composite = 1
prime factor = 2
prime factor = 3
22 = 4
prime factor = 5
2 × 3 = 6
23 = 8
32 = 9
2 × 5 = 10
prime factor = 11
22 × 3 = 12
3 × 5 = 15
continued below...
... continued from above
24 = 16
2 × 32 = 18
22 × 5 = 20
2 × 11 = 22
23 × 3 = 24
52 = 25
33 = 27
2 × 3 × 5 = 30
25 = 32
3 × 11 = 33
22 × 32 = 36
23 × 5 = 40
22 × 11 = 44
32 × 5 = 45
24 × 3 = 48
2 × 52 = 50
2 × 33 = 54
5 × 11 = 55
22 × 3 × 5 = 60
26 = 64
2 × 3 × 11 = 66
23 × 32 = 72
3 × 52 = 75
24 × 5 = 80
23 × 11 = 88
2 × 32 × 5 = 90
25 × 3 = 96
32 × 11 = 99
22 × 52 = 100
22 × 33 = 108
2 × 5 × 11 = 110
23 × 3 × 5 = 120
53 = 125
22 × 3 × 11 = 132
33 × 5 = 135
24 × 32 = 144
2 × 3 × 52 = 150
25 × 5 = 160
3 × 5 × 11 = 165
24 × 11 = 176
22 × 32 × 5 = 180
26 × 3 = 192
2 × 32 × 11 = 198
23 × 52 = 200
23 × 33 = 216
22 × 5 × 11 = 220
32 × 52 = 225
24 × 3 × 5 = 240
2 × 53 = 250
23 × 3 × 11 = 264
2 × 33 × 5 = 270
52 × 11 = 275
25 × 32 = 288
33 × 11 = 297
22 × 3 × 52 = 300
26 × 5 = 320
2 × 3 × 5 × 11 = 330
25 × 11 = 352
23 × 32 × 5 = 360
3 × 53 = 375
22 × 32 × 11 = 396
24 × 52 = 400
24 × 33 = 432
23 × 5 × 11 = 440
2 × 32 × 52 = 450
25 × 3 × 5 = 480
32 × 5 × 11 = 495
22 × 53 = 500
24 × 3 × 11 = 528
22 × 33 × 5 = 540
2 × 52 × 11 = 550
26 × 32 = 576
2 × 33 × 11 = 594
23 × 3 × 52 = 600
22 × 3 × 5 × 11 = 660
33 × 52 = 675
26 × 11 = 704
24 × 32 × 5 = 720
2 × 3 × 53 = 750
23 × 32 × 11 = 792
25 × 52 = 800
3 × 52 × 11 = 825
25 × 33 = 864
24 × 5 × 11 = 880
22 × 32 × 52 = 900
26 × 3 × 5 = 960
2 × 32 × 5 × 11 = 990
23 × 53 = 1,000
25 × 3 × 11 = 1,056
23 × 33 × 5 = 1,080
22 × 52 × 11 = 1,100
32 × 53 = 1,125
22 × 33 × 11 = 1,188
24 × 3 × 52 = 1,200
23 × 3 × 5 × 11 = 1,320
2 × 33 × 52 = 1,350
53 × 11 = 1,375
25 × 32 × 5 = 1,440
33 × 5 × 11 = 1,485
22 × 3 × 53 = 1,500
24 × 32 × 11 = 1,584
26 × 52 = 1,600
2 × 3 × 52 × 11 = 1,650
26 × 33 = 1,728
25 × 5 × 11 = 1,760
23 × 32 × 52 = 1,800
22 × 32 × 5 × 11 = 1,980
24 × 53 = 2,000
26 × 3 × 11 = 2,112
24 × 33 × 5 = 2,160
23 × 52 × 11 = 2,200
2 × 32 × 53 = 2,250
23 × 33 × 11 = 2,376
25 × 3 × 52 = 2,400
32 × 52 × 11 = 2,475
24 × 3 × 5 × 11 = 2,640
22 × 33 × 52 = 2,700
2 × 53 × 11 = 2,750
26 × 32 × 5 = 2,880
2 × 33 × 5 × 11 = 2,970
23 × 3 × 53 = 3,000
25 × 32 × 11 = 3,168
22 × 3 × 52 × 11 = 3,300
33 × 53 = 3,375
26 × 5 × 11 = 3,520
24 × 32 × 52 = 3,600
23 × 32 × 5 × 11 = 3,960
25 × 53 = 4,000
3 × 53 × 11 = 4,125
25 × 33 × 5 = 4,320
24 × 52 × 11 = 4,400
22 × 32 × 53 = 4,500
24 × 33 × 11 = 4,752
26 × 3 × 52 = 4,800
2 × 32 × 52 × 11 = 4,950
25 × 3 × 5 × 11 = 5,280
23 × 33 × 52 = 5,400
22 × 53 × 11 = 5,500
22 × 33 × 5 × 11 = 5,940
24 × 3 × 53 = 6,000
26 × 32 × 11 = 6,336
23 × 3 × 52 × 11 = 6,600
2 × 33 × 53 = 6,750
25 × 32 × 52 = 7,200
33 × 52 × 11 = 7,425
24 × 32 × 5 × 11 = 7,920
26 × 53 = 8,000
2 × 3 × 53 × 11 = 8,250
26 × 33 × 5 = 8,640
25 × 52 × 11 = 8,800
23 × 32 × 53 = 9,000
25 × 33 × 11 = 9,504
22 × 32 × 52 × 11 = 9,900
26 × 3 × 5 × 11 = 10,560
24 × 33 × 52 = 10,800
23 × 53 × 11 = 11,000
23 × 33 × 5 × 11 = 11,880
25 × 3 × 53 = 12,000
32 × 53 × 11 = 12,375
24 × 3 × 52 × 11 = 13,200
22 × 33 × 53 = 13,500
26 × 32 × 52 = 14,400
2 × 33 × 52 × 11 = 14,850
25 × 32 × 5 × 11 = 15,840
22 × 3 × 53 × 11 = 16,500
26 × 52 × 11 = 17,600
24 × 32 × 53 = 18,000
26 × 33 × 11 = 19,008
23 × 32 × 52 × 11 = 19,800
25 × 33 × 52 = 21,600
24 × 53 × 11 = 22,000
24 × 33 × 5 × 11 = 23,760
26 × 3 × 53 = 24,000
2 × 32 × 53 × 11 = 24,750
25 × 3 × 52 × 11 = 26,400
23 × 33 × 53 = 27,000
22 × 33 × 52 × 11 = 29,700
26 × 32 × 5 × 11 = 31,680
23 × 3 × 53 × 11 = 33,000
25 × 32 × 53 = 36,000
33 × 53 × 11 = 37,125
24 × 32 × 52 × 11 = 39,600
26 × 33 × 52 = 43,200
25 × 53 × 11 = 44,000
25 × 33 × 5 × 11 = 47,520
22 × 32 × 53 × 11 = 49,500
26 × 3 × 52 × 11 = 52,800
24 × 33 × 53 = 54,000
23 × 33 × 52 × 11 = 59,400
24 × 3 × 53 × 11 = 66,000
26 × 32 × 53 = 72,000
2 × 33 × 53 × 11 = 74,250
25 × 32 × 52 × 11 = 79,200
26 × 53 × 11 = 88,000
26 × 33 × 5 × 11 = 95,040
23 × 32 × 53 × 11 = 99,000
25 × 33 × 53 = 108,000
24 × 33 × 52 × 11 = 118,800
25 × 3 × 53 × 11 = 132,000
22 × 33 × 53 × 11 = 148,500
26 × 32 × 52 × 11 = 158,400
24 × 32 × 53 × 11 = 198,000
26 × 33 × 53 = 216,000
25 × 33 × 52 × 11 = 237,600
26 × 3 × 53 × 11 = 264,000
23 × 33 × 53 × 11 = 297,000
25 × 32 × 53 × 11 = 396,000
26 × 33 × 52 × 11 = 475,200
24 × 33 × 53 × 11 = 594,000
26 × 32 × 53 × 11 = 792,000
25 × 33 × 53 × 11 = 1,188,000
26 × 33 × 53 × 11 = 2,376,000

Final answer:

7,128,000 and 11,880,000 have 224 common factors (divisors):
1; 2; 3; 4; 5; 6; 8; 9; 10; 11; 12; 15; 16; 18; 20; 22; 24; 25; 27; 30; 32; 33; 36; 40; 44; 45; 48; 50; 54; 55; 60; 64; 66; 72; 75; 80; 88; 90; 96; 99; 100; 108; 110; 120; 125; 132; 135; 144; 150; 160; 165; 176; 180; 192; 198; 200; 216; 220; 225; 240; 250; 264; 270; 275; 288; 297; 300; 320; 330; 352; 360; 375; 396; 400; 432; 440; 450; 480; 495; 500; 528; 540; 550; 576; 594; 600; 660; 675; 704; 720; 750; 792; 800; 825; 864; 880; 900; 960; 990; 1,000; 1,056; 1,080; 1,100; 1,125; 1,188; 1,200; 1,320; 1,350; 1,375; 1,440; 1,485; 1,500; 1,584; 1,600; 1,650; 1,728; 1,760; 1,800; 1,980; 2,000; 2,112; 2,160; 2,200; 2,250; 2,376; 2,400; 2,475; 2,640; 2,700; 2,750; 2,880; 2,970; 3,000; 3,168; 3,300; 3,375; 3,520; 3,600; 3,960; 4,000; 4,125; 4,320; 4,400; 4,500; 4,752; 4,800; 4,950; 5,280; 5,400; 5,500; 5,940; 6,000; 6,336; 6,600; 6,750; 7,200; 7,425; 7,920; 8,000; 8,250; 8,640; 8,800; 9,000; 9,504; 9,900; 10,560; 10,800; 11,000; 11,880; 12,000; 12,375; 13,200; 13,500; 14,400; 14,850; 15,840; 16,500; 17,600; 18,000; 19,008; 19,800; 21,600; 22,000; 23,760; 24,000; 24,750; 26,400; 27,000; 29,700; 31,680; 33,000; 36,000; 37,125; 39,600; 43,200; 44,000; 47,520; 49,500; 52,800; 54,000; 59,400; 66,000; 72,000; 74,250; 79,200; 88,000; 95,040; 99,000; 108,000; 118,800; 132,000; 148,500; 158,400; 198,000; 216,000; 237,600; 264,000; 297,000; 396,000; 475,200; 594,000; 792,000; 1,188,000 and 2,376,000
out of which 4 prime factors: 2; 3; 5 and 11

The key to find the divisors of a number is to build its prime factorization.


Then determine all the different combinations (multiplications) of the prime factors, and their exponents, if any.



More operations of this kind:

Calculator: all the (common) factors (divisors) of numbers

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Tutoring: factors (divisors), common factors (common divisors), the greatest common factor, GCF (also called the greatest common divisor, GCD, or the highest common factor, HCF)

If "t" is a factor (divisor) of "a" then among the prime factors of "t" will appear only prime factors that also appear on the prime factorization of "a" and the maximum of their exponents (powers, or multiplicities) is at most equal to those involved in the prime factorization of "a".

For example, 12 is a factor (divisor) of 60:

  • 12 = 2 × 2 × 3 = 22 × 3
  • 60 = 2 × 2 × 3 × 5 = 22 × 3 × 5

If "t" is a common factor (divisor) of "a" and "b", then the prime factorization of "t" contains only the common prime factors involved in both the prime factorizations of "a" and "b", by lower or at most by equal powers (exponents, or multiplicities).

For example, 12 is the common factor of 48 and 360. After running both numbers' prime factorizations (factoring them down to prime factors):

  • 12 = 22 × 3;
  • 48 = 24 × 3;
  • 360 = 23 × 32 × 5;
  • Please note that 48 and 360 have more factors (divisors): 2, 3, 4, 6, 8, 12, 24. Among them, 24 is the greatest common factor, GCF (or the greatest common divisor, GCD, or the highest common factor, HCF) of 48 and 360.

The greatest common factor, GCF, is the product of all prime factors involved in both the prime factorizations of "a" and "b", by the lowest powers (multiplicities).

Based on this rule it is calculated the greatest common factor, GCF, (or greatest common divisor GCD, HCF) of several numbers, as shown in the example below:

  • 1,260 = 22 × 32;
  • 3,024 = 24 × 32 × 7;
  • 5,544 = 23 × 32 × 7 × 11;
  • Common prime factors are: 2 - its lowest power (multiplicity) is min.(2; 3; 4) = 2; 3 - its lowest power (multiplicity) is min.(2; 2; 2) = 2;
  • GCF, GCD (1,260; 3,024; 5,544) = 22 × 32 = 252;

If two numbers "a" and "b" have no other common factors (divisors) than 1, gfc, gcd, hcf (a; b) = 1, then the numbers "a" and "b" are called coprime (or relatively prime).

If "a" and "b" are not coprime, then every common factor (divisor) of "a" and "b" is a also a factor (divisor) of the greatest common factor, GCF (greatest common divisor, GCD, highest common factor, HCF) of "a" and "b".


What is a prime number?

What is a composite number?

Prime numbers up to 1,000

Prime numbers up to 10,000

Sieve of Eratosthenes

Euclid's algorithm

Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples